1. Technical Field
The present invention relates to deforming images, and more particularly to a system and method for deforming images using physical models.
2. Discussion of Related Art
As-rigid-as-possible image deformations produce intuitive results when a user wants to manually control the shape deformation of an image. As-rigid-as-possible transformations, introduced for the purpose of shape interpolation, are characterized by a minimum amount of scaling and shearing. Such transformations mimic the adaptation of the mechanical properties (e.g., the stiffness) of the transformation to enforce rigidity.
In the context of image deformation as-rigid-as-possible transformations have been introduced to avoid undesirable effects like folding and non-uniform scaling typically perceived in previous methods. The particular properties of as-rigid-as-possible transformations have been enforced by minimizing the distortion of triangular elements in a 2D mesh. By separating the rotational part from the scaling the problem is decomposed into the solution of two least squares problems. In principle, this technique can be seen as a variant of constraint mesh deformation techniques, which pose the problem of shape deformation as an energy minimization problem. Such techniques
have been used successfully for shape-preserving 3D mesh deformation, and in the context of image deformation.
The idea of shape-preserving deformations has been built upon using a rotation invariant shape representation constraint by a set of angles and lengths relating a vertex to its immediate neighbors. Another method for inhomogeneous texture mapping is based on a classification of cells into rigid and elastic. Determining the global displacement field can then be posed as an optimization problem that takes into account the specific cell properties as additional constraints.
Although as-rigid-as-possible transformations are well suited for the purpose of shape preservation they are not effective at following physics-based constraints like volume preservation or elastic deformations. As images are typically composed of parts, it is often desired to continuously adjust the stiffness of the transformation to permit larger displacements over parts that are known to be compliant and smaller displacements over parts that are known to be less compliant.
Therefore, a need exists for an efficient image deformation method using physical models together with as-rigid-as-possible transformations.